Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states

TL;DR

This paper develops a formalism to establish ultimate classical benchmarks for quantum information protocols involving generalized coherent and squeezed states, enabling the certification of quantum advantage in communication tasks.

Contribution

It introduces a self-contained method to derive probabilistic fidelity benchmarks for diverse quantum states, facilitating the validation of quantum technologies against classical limits.

Findings

Derived explicit fidelity thresholds for Gaussian and non-Gaussian states.

Compared classical strategies with optimal probabilistic benchmarks.

Assessed current quantum implementations against new benchmarks.

Abstract

Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.